A - is the numerical coefficient of the quadratic term (i.e the number just in front of x2)

B - is the numerical coefficient of the linear term (i.e the number just in front of x )

For example :
For 2x2 + 5x + 3 = 0
2 is the number in front of x2 ,so 2 is the numerical coeffient of
the quadratic term or the coefficient of x2

5 is the number in front of x , so 5 is the numerical coefficient of the linear term or the coefficient of x

and 3 is the constant term.

Now for x2 + x + 3 = 0
since x2 + x + 3 = 1x2 + 1x + 3

1 is the number in front of x2 , so 1 is the numerical coefficient of the quadratic term or 1 is the coefficient of x2

1 is the number in front of x , so 1 is the numerical coefficient of the linear term or 1 is the coefficient of x

and 3 is the constant term.

Note : that 2 times x = 2x
following from that we could have 1 times x = 1x
but since 1 times 5 = 5 or a number times 1 is the number itself
we normally write 1 times x = x instead of 1x.
So if you have any variable x it is understood to be 1x
so that the coefficient of x is the number in front of x which is 1.
when you see no number in front of the variable x since x is really 1x
the number infront of x is 1 or the coefficient of x is 1.
similarly for x2 , 1 is the coefficient of x2
for y ,1 is the coefficient of y,
for y2 ,1 is the coefficient of y2 etc..